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Problem of the Month - September 2024

The diagonal of this 3 x 5 grid goes through 7 squares.  

How many squares would the diagonal of a 12 x 20 grid go through?  

What about a 6 x 9 grid?  

A three by five grid of squares that includes a diagonal from the top left to the bottom right

Solution

In a 12 x 20 grid, the diagonal would go through 28 squares.  In a 6 x 9 grid, the diagonal would go through 12 squares.  

Can you generalise your answer for an n x m grid?  

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